The lifespans of porcupines in a particular zoo are normally distributed. The average porcupine lives $16.8$ years; the standard deviation is $1.9$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a porcupine living between $14.9$ and $18.7$ years.
Answer: $16.8$ $14.9$ $18.7$ $13$ $20.6$ $11.1$ $22.5$ $68\%$ We know the lifespans are normally distributed with an average lifespan of $16.8$ years. We know the standard deviation is $1.9$ years, so one standard deviation below the mean is $14.9$ years and one standard deviation above the mean is $18.7$ years. Two standard deviations below the mean is $13$ years and two standard deviations above the mean is $20.6$ years. Three standard deviations below the mean is $11.1$ years and three standard deviations above the mean is $22.5$ years. We are interested in the probability of a porcupine living between $14.9$ and $18.7$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $68\%$ of the porcupines will have lifespans within 1 standard deviation of the average lifespan. The probability of a particular porcupine living between $14.9$ and $18.7$ years is ${68\%}$.